document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69074>Question 69074</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395430542/algebrahomeworkh>Algebra and Trigonometry: Structure and Method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> When Acme Airlines changed to planes that could fly 100 km/h faster than its old ones, the time of its 2800 km Dallas-Seattle flight was reduced by 30 minutes. Find the speed of the new planes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49156 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=49156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x= speed of old ones\r<BR>\n" );
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document.write( "x+100= speed of new ones\r<BR>\n" );
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document.write( "distance (d)=rate(r) times time (t) or d=rt and t=d/r\r<BR>\n" );
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document.write( "2800/x= time it took old planes to make the trip\r<BR>\n" );
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document.write( "2800/(x+100)= time it takes the new planes to make the trip\r<BR>\n" );
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document.write( "Now we are told that the new planes make the trip 30 min (0.5 hr) faster than the old planes.  So our equation to solve is:\r<BR>\n" );
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document.write( "2800/x=(2800/(x+100))+0.5   multiply both sides by x(x+100)\r<BR>\n" );
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document.write( "2800(x+100)=2800x+0.5x(x+100)  clear parens\r<BR>\n" );
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document.write( "2800x+280000=2800x+0.5x^2+50x  subtract 2800x and also 280000 from both sides\r<BR>\n" );
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document.write( "2800x-2800x+280000-280000=2800x-2800x-280000+0.5x^2+50x  collect like terms\r<BR>\n" );
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document.write( "0=0.5x^2+50x-280000 or  multiply both sides by 2\r<BR>\n" );
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document.write( "x^2+100x-560000=0   Quadratic in standard form\r<BR>\n" );
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document.write( "This quadratic can be factored:\r<BR>\n" );
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document.write( "(x+800)(x-700)=0\r<BR>\n" );
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document.write( "discount negative value for speed\r<BR>\n" );
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document.write( "So <BR>\n" );
document.write( "x=700 km/hr ------------------------------speed of old planes\r<BR>\n" );
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document.write( "x+100=800 km/hr speed of new planes\r<BR>\n" );
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document.write( "Ck\r<BR>\n" );
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document.write( "2800/x=4 hrs <BR>\n" );
document.write( "2800/(x+100)=3.5 hrs-----30 min less ---checks\r<BR>\n" );
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document.write( "Hope this helps----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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